This work develops, for the first time, a face-centred finite volume (FCFV) solver for the simulation of laminar and turbulent viscous incompressible flows. The formulation relies on the Reynolds-averaged Navier-Stokes (RANS) equations coupled with the negative Spalart-Allmaras (SA) model and three novel convective stabilisations, inspired by Riemann solvers, are derived and compared numerically. The resulting method achieves first-order convergence of the velocity, the velocity-gradient tensor and the pressure. FCFV accurately predicts engineering quantities of interest, such as drag and lift, on unstructured meshes and, by avoiding gradient reconstruction, the method is insensitive to mesh quality, even in the presence of highly distorted and stretched cells. A monolithic and a staggered solution strategies for the RANS-SA system are derived and compared numerically. Numerical benchmarks, involving laminar and turbulent, steady and transient cases are used to assess the performance, accuracy and robustness of the proposed FCFV method.

翻译：本文首次提出一种面向层流与湍流黏性不可压缩流动模拟的面心有限体积（FCFV）求解器。该公式基于雷诺平均纳维-斯托克斯（RANS）方程，耦合负Spalart-Allmaras（SA）湍流模型，并推导出三种受黎曼求解器启发的新型对流稳定化方法，通过数值比较评估其性能。所提方法实现了速度、速度梯度张量及压力的一阶收敛精度。FCFV能在非结构化网格上准确预测阻力、升力等工程关注量，且由于避免了梯度重构，该方法对网格质量不敏感，即使存在高度畸变及拉伸单元仍保持稳健性。针对RANS-SA系统，分别推导了整体求解策略与交错求解策略并进行数值对比。通过涵盖层流/湍流、稳态/瞬态工况的数值基准算例，全面评估了所提FCFV方法的性能、精度与鲁棒性。